Simple Flower

Geometry Level 1

What fraction of this flower's face is blue?

1 2 \frac12 2 3 \frac23 3 5 \frac35 2 5 \frac25

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6 solutions

Zandra Vinegar Staff
Sep 30, 2015

There are 6 blue rhombuses and 6 red trapezoids. So, by symmetry and imagining these shapes split into congruent equilateral triangles, 2 out of every 5 triangles are blue.

Exactly how I did it man

Oscar Shen - 5 years, 8 months ago

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Simplicity is Beautiful

Sam Lee - 5 years, 8 months ago
Gary Aknin
Oct 1, 2015

Answer: 2/5 Rhombus with sides 1 unit and angles 60, 120, 60, and 120 degrees.

Area of Rhombus: base * height where height = cos(30) and base = 1 cos(30)*1 = = sqrt(3)/2 * 1 = sqrt(3)/2

Area of Trapizoid: base * hight where height = cos(30) = sqrt(3)/2 base = 1 + sin(30) = 1 + .5 = 1.5

Area = 1.5 * sqrt(3)/2

Ratio of Rhombus / (rhombus + trapezoid) = sqrt(3)/2 / (sqrt(3)/2 + 1.5 * sqrt(3)/2) = 1/2.5 = 2/5

Basic common sense that rest of the options cannot be true since its so evident that blue part is less than half.

We can convert the red trapezoid into 3 blue triangle -the half of the blue rhombus- so we'll get a total of 30 blue size triangles

12 30 = 2 5 \frac{12}{30}=\frac25

We can divide it into 30 congruent triangles, We can divide blue triangles into 6 congruent tiriangles, So fraction of blue triangle = 12/30 = 2/5

Chris White
Oct 1, 2015

blue is 1, orange is 1.5 so blue is 6/15 or 2/5.

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